Furstenberg-type estimates for unions of affine subspaces

Fractal Geometry and Dynamics

16 November 15:00 - 15:50

Kornélia Héra - Eötvös Loránd University

A compact plane set is a t-Furstenberg set for some t in (0,1), if it has an at least t-dimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension). Classical results are that every t-Furstenberg set has dimension at least 2t, and at least t + 1/2. We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any s-dimensional family of k-dimensional affine subspaces is at least k + s/(k+1) -dimensional, and is exactly k + s -dimensional if s is at most 1. Joint work with Tamás Keleti and András Máthé.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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